What is the derivative of (20x^2/((x-1)^3)) ?

The derivative of (20x^2/((x-1)^3)) is (20x(-x-2))/((x-1)^4)

What is the first derivative of (20x^2/((x-1)^3)) ?

The first derivative of (20x^2/((x-1)^3)) is (20x(-x-2))/((x-1)^4)

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\frac{d}{d x} (\frac{20 x ^{2}}{( x - 1 ) ^{3}})

\frac{20 x ( - x - 2 )}{( x - 1 ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{20 x ^{2}}{( x - 1 ) ^{3}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 20 \frac{d}{d x} (\frac{x ^{2}}{( x - 1 ) ^{3}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 20 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( x - 1 ) ^{3} - \frac{d}{d x} ( ( x - 1 ) ^{3} ) x ^{2}}{( ( x - 1 ) ^{3} ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} ((x - 1)^{3}) = 3 (x - 1)^{2}

= 20 \cdot \frac{2 x ( x - 1 ) ^{3} - 3 ( x - 1 ) ^{2} x ^{2}}{( ( x - 1 ) ^{3} ) ^{2}}

Simplify

20 \cdot \frac{2 x ( x - 1 ) ^{3} - 3 ( x - 1 ) ^{2} x ^{2}}{( ( x - 1 ) ^{3} ) ^{2}} : \frac{20 x ( - x - 2 )}{( x - 1 ) ^{4}}

= \frac{20 x ( - x - 2 )}{( x - 1 ) ^{4}}

What is the derivative of (20x^2/((x-1)^3)) ?
The derivative of (20x^2/((x-1)^3)) is (20x(-x-2))/((x-1)^4)
What is the first derivative of (20x^2/((x-1)^3)) ?
The first derivative of (20x^2/((x-1)^3)) is (20x(-x-2))/((x-1)^4)